{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:2VJEDIQAJA2VJHQSTY5335BLSR","short_pith_number":"pith:2VJEDIQA","canonical_record":{"source":{"id":"2505.09793","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-14T20:41:59Z","cross_cats_sorted":[],"title_canon_sha256":"325c1fa3c8de65af639e5cbc565a0fe4785ce87f52560016f194dd708d3f8cc0","abstract_canon_sha256":"4619cd91a99b781ca9b8811e713c08bce9a6a12109e73abf00a47b0133ef01ed"},"schema_version":"1.0"},"canonical_sha256":"d55241a2004835549e129e3bbdf42b945d5380c79a14058571e3639f3ad8c07e","source":{"kind":"arxiv","id":"2505.09793","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.09793","created_at":"2026-07-05T11:03:28Z"},{"alias_kind":"arxiv_version","alias_value":"2505.09793v1","created_at":"2026-07-05T11:03:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.09793","created_at":"2026-07-05T11:03:28Z"},{"alias_kind":"pith_short_12","alias_value":"2VJEDIQAJA2V","created_at":"2026-07-05T11:03:28Z"},{"alias_kind":"pith_short_16","alias_value":"2VJEDIQAJA2VJHQS","created_at":"2026-07-05T11:03:28Z"},{"alias_kind":"pith_short_8","alias_value":"2VJEDIQA","created_at":"2026-07-05T11:03:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:2VJEDIQAJA2VJHQSTY5335BLSR","target":"record","payload":{"canonical_record":{"source":{"id":"2505.09793","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-14T20:41:59Z","cross_cats_sorted":[],"title_canon_sha256":"325c1fa3c8de65af639e5cbc565a0fe4785ce87f52560016f194dd708d3f8cc0","abstract_canon_sha256":"4619cd91a99b781ca9b8811e713c08bce9a6a12109e73abf00a47b0133ef01ed"},"schema_version":"1.0"},"canonical_sha256":"d55241a2004835549e129e3bbdf42b945d5380c79a14058571e3639f3ad8c07e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:03:28.730087Z","signature_b64":"VnzcBskXukpW9bNdePCVkmQLqYD6legodgZLhZhqrYyTzUo3CmyWBAttgXLqROKYCiyurAqMJeGN/sA+Q8yBBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d55241a2004835549e129e3bbdf42b945d5380c79a14058571e3639f3ad8c07e","last_reissued_at":"2026-07-05T11:03:28.729618Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:03:28.729618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.09793","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:03:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dTp3C0qCV5GijUmWG18SEptOQ51tSOq3M3K+SwUH4a73PaL1MvRdMY55/TdFzzNI7BcuINaUtrwP1+fUQ3RvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T16:30:05.492030Z"},"content_sha256":"1f2a7e91261aae25591183da79eb8ac7577fce2f87a8c51946bdaffd8ef34767","schema_version":"1.0","event_id":"sha256:1f2a7e91261aae25591183da79eb8ac7577fce2f87a8c51946bdaffd8ef34767"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:2VJEDIQAJA2VJHQSTY5335BLSR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Arbitrary orientations of Hamilton cycles in directed graphs of large minimum degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrew Treglown, Louis DeBiasio","submitted_at":"2025-05-14T20:41:59Z","abstract_excerpt":"In 1960, Ghouila-Houri proved that every strongly connected directed graph $G$ on $n$ vertices with minimum degree at least $n$ contains a directed Hamilton cycle. We asymptotically generalize this result by proving the following: every directed graph $G$ on $n$ vertices and with minimum degree at least $(1+o(1))n$ contains every orientation of a Hamilton cycle, except for the directed Hamilton cycle in the case when $G$ is not strongly connected. In fact, this minimum degree condition forces every orientation of a cycle in $G$ of every possible length, other than perhaps the directed cycles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.09793","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.09793/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:03:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8iHzD8mjoM+qnNMKEGjxPC21SsXT73WGmKuLTb9Un+uA0gaT/vuJADfDfPv879DvU/Z0FCVLKrVH5n6egeLTDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T16:30:05.492539Z"},"content_sha256":"7fedd029bb206ed1ccd2a8c22adcf4e01c967f776af2311acd61b905e188f605","schema_version":"1.0","event_id":"sha256:7fedd029bb206ed1ccd2a8c22adcf4e01c967f776af2311acd61b905e188f605"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2VJEDIQAJA2VJHQSTY5335BLSR/bundle.json","state_url":"https://pith.science/pith/2VJEDIQAJA2VJHQSTY5335BLSR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2VJEDIQAJA2VJHQSTY5335BLSR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-16T16:30:05Z","links":{"resolver":"https://pith.science/pith/2VJEDIQAJA2VJHQSTY5335BLSR","bundle":"https://pith.science/pith/2VJEDIQAJA2VJHQSTY5335BLSR/bundle.json","state":"https://pith.science/pith/2VJEDIQAJA2VJHQSTY5335BLSR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2VJEDIQAJA2VJHQSTY5335BLSR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:2VJEDIQAJA2VJHQSTY5335BLSR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4619cd91a99b781ca9b8811e713c08bce9a6a12109e73abf00a47b0133ef01ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-14T20:41:59Z","title_canon_sha256":"325c1fa3c8de65af639e5cbc565a0fe4785ce87f52560016f194dd708d3f8cc0"},"schema_version":"1.0","source":{"id":"2505.09793","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.09793","created_at":"2026-07-05T11:03:28Z"},{"alias_kind":"arxiv_version","alias_value":"2505.09793v1","created_at":"2026-07-05T11:03:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.09793","created_at":"2026-07-05T11:03:28Z"},{"alias_kind":"pith_short_12","alias_value":"2VJEDIQAJA2V","created_at":"2026-07-05T11:03:28Z"},{"alias_kind":"pith_short_16","alias_value":"2VJEDIQAJA2VJHQS","created_at":"2026-07-05T11:03:28Z"},{"alias_kind":"pith_short_8","alias_value":"2VJEDIQA","created_at":"2026-07-05T11:03:28Z"}],"graph_snapshots":[{"event_id":"sha256:7fedd029bb206ed1ccd2a8c22adcf4e01c967f776af2311acd61b905e188f605","target":"graph","created_at":"2026-07-05T11:03:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.09793/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In 1960, Ghouila-Houri proved that every strongly connected directed graph $G$ on $n$ vertices with minimum degree at least $n$ contains a directed Hamilton cycle. We asymptotically generalize this result by proving the following: every directed graph $G$ on $n$ vertices and with minimum degree at least $(1+o(1))n$ contains every orientation of a Hamilton cycle, except for the directed Hamilton cycle in the case when $G$ is not strongly connected. In fact, this minimum degree condition forces every orientation of a cycle in $G$ of every possible length, other than perhaps the directed cycles.","authors_text":"Andrew Treglown, Louis DeBiasio","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-14T20:41:59Z","title":"Arbitrary orientations of Hamilton cycles in directed graphs of large minimum degree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.09793","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1f2a7e91261aae25591183da79eb8ac7577fce2f87a8c51946bdaffd8ef34767","target":"record","created_at":"2026-07-05T11:03:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4619cd91a99b781ca9b8811e713c08bce9a6a12109e73abf00a47b0133ef01ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-14T20:41:59Z","title_canon_sha256":"325c1fa3c8de65af639e5cbc565a0fe4785ce87f52560016f194dd708d3f8cc0"},"schema_version":"1.0","source":{"id":"2505.09793","kind":"arxiv","version":1}},"canonical_sha256":"d55241a2004835549e129e3bbdf42b945d5380c79a14058571e3639f3ad8c07e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d55241a2004835549e129e3bbdf42b945d5380c79a14058571e3639f3ad8c07e","first_computed_at":"2026-07-05T11:03:28.729618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:03:28.729618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VnzcBskXukpW9bNdePCVkmQLqYD6legodgZLhZhqrYyTzUo3CmyWBAttgXLqROKYCiyurAqMJeGN/sA+Q8yBBg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:03:28.730087Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.09793","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f2a7e91261aae25591183da79eb8ac7577fce2f87a8c51946bdaffd8ef34767","sha256:7fedd029bb206ed1ccd2a8c22adcf4e01c967f776af2311acd61b905e188f605"],"state_sha256":"eea0e3cd79deca619eed32f3246b890210c3bfb0d24775662cc7ee6c16489492"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VtX1Ipo2/NjNfloHf9Hu5mfVgmXqmneVCCxMYdP1hbX3gzmWhl9iaDU/SVKPYdffqb7DcKpSU/+jcERahQcyDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T16:30:05.497538Z","bundle_sha256":"9e7f1a43d1f9fd660a733e8228f554c9a8f7972a2e0f97f741acde162f27a029"}}